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DOI: 10.1016/j.physletb.2015.11.042
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DIRETORIA DE TRATAMENTO DA INFORMAÇÃO
Cidade Universitária Zeferino Vaz Barão Geraldo
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Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Search
for
neutral
MSSM
Higgs
bosons
decaying
to
μ
+
μ
−
in
pp
collisions
at
√
s
=
7 and 8 TeV
.
CMS
Collaboration
CERN,Switzerland
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received6August2015
Receivedinrevisedform2November2015 Accepted10November2015
Availableonline23November2015 Editor:M.Doser Keywords: CMS Physics Higgs MSSM Dimuons
A searchfor neutralHiggs bosonspredicted inthe minimalsupersymmetricstandard model (MSSM) for
μ
+μ
−decaychannelsispresented.Theanalysisusesdata collectedbytheCMSexperimentatthe LHCinproton–protoncollisionsatcentre-of-massenergiesof7and8 TeV,correspondingtointegrated luminositiesof5.1and19.3 fb−1,respectively.ThesearchissensitivetoHiggsbosonsproducedeither throughthegluonfusionprocessorinassociationwithabb quarkpair.Nostatisticallysignificantexcess isobservedintheμ
+μ
−massspectrum.Resultsareinterpretedintheframeworkofseveralbenchmark scenarios,andthedataareusedtosetanupperlimitontheMSSMparametertanβasafunctionofthe massofthepseudoscalarAbosonintherangefrom115to300 GeV.Modelindependentupperlimitsare givenfortheproductofthecrosssectionandbranchingfractionforgluonfusionandbquarkassociated productionat√s=8 TeV.Theyarethemoststringentlimitsobtainedtodateinthischannel.©2015CERNforthebenefitoftheCMSCollaboration.PublishedbyElsevierB.V.Thisisanopenaccess articleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
The predictions of the standard model (SM) [1–7] of funda-mental interactions have been confirmed by a large number of experimentalmeasurements.Theobservationofanewbosonwith amassof125 GeVandpropertiescompatiblewiththoseoftheSM Higgs boson [8–10] confirms the mechanism of the electroweak symmetrybreaking (EWSB).Despitethe successofthistheory in describingthe phenomenology of particlephysics atpresent col-lider energies, the mass of the Higgs boson in the SM is not protectedagainstquadraticallydivergentquantum-loopcorrections athighenergy. Supersymmetry(SUSY) [11,12]is one exampleof alternativemodelsthataddressthisproblem.InSUSY,such diver-gences are cancelledby introducing a symmetry between funda-mentalbosonsandfermions.
Theminimal supersymmetricextensionofthe standardmodel (MSSM)[13,14]predictstheexistenceoftwoHiggsdoubletfields. Onedoublet couples to up-typeandone to down-typefermions. AfterEWSB, fivephysical Higgsbosons remain: a CP-oddneutral scalarA,two chargedscalarsH±,andtwoCP-evenneutralscalar particlesh and H.Theneutralbosons h,A,andH,willbe gener-icallyreferredto as
φ
collectivelyinthispaper,unlessdifferently specified.E-mailaddress:cms-publication-committee-chair@cern.ch.
Atlowestorderinperturbationtheory,theHiggssectorinthe MSSMcanbedescribed intermsoftwofreeparameters:mA,the
massoftheneutralpseudoscalarA,andtan
β
,theratioofthe vac-uum expectationvaluesofthetwoHiggsdoublets.Themassesof the other fourHiggs bosons can be expressed in terms of these twoparametersandothermeasuredquantities,suchasthemasses mW and mZ of the W and Z bosons, respectively. In particular,themassesoftheneutralMSSMscalarHiggsbosonsH andh are given[13]by mH,h
=
1 2 m2A+
m2Z±
m2A+
m2Z2−
4m2Am2Zcos22β
1/21/2
.
(1)The Aand H bosonsare degenerate inmass above140 GeV and forsmall cos
β
(large tanβ
) values.Thisexpression alsoprovides an upperbound onthemassofthelightscalarHiggsboson, cor-responding to mh≤
mZ|
cos 2β
|
. The value can become as largeas mh
≈
135 GeV once radiative corrections are taken intoac-count[15].
The main production mechanisms for the three neutral
φ
bosons at theLHC are the associated productionwith bb quarks (AP), given atthe leading order by the Feynman diagram shown inFig. 1(top),andthegluon fusion(GF)process,showninFig. 1 (bottom)[16–18].TheGFprocesswithvirtualtorbquarksinthe http://dx.doi.org/10.1016/j.physletb.2015.11.042
0370-2693/©2015CERNforthebenefitoftheCMSCollaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
Fig. 1. Leading-orderdiagramsforthemainproductionprocessesofMSSMHiggs bosonsattheLHC(top)inassociationwith bb productionand(bottom)through gluonfusion.
loop isdominantatsmallandmoderatevalues oftan
β
. Atlarge tanβ
thecouplingofφ
todown-typequarksisenhancedrelative to theSM [19] andtheAP process becomes dominant. Similarly, thecouplingoftheφ
bosontochargedleptonsisalsoenhancedat largetanβ
.This paper reports on a search for the MSSM neutral Higgs bosons produced eitherby the APorGFmechanisms, wherethe Higgs bosons decay via
φ
→
μ
+μ
−. The analysis is sensitive to allthe threebosons, h,H,andAinthe massrangebetween115 and300 GeV. The search is performedby theCMS collaboration usingdatarecordedin ppcollisions attheLHC,corresponding to anintegratedluminosityof5.1 fb−1at√
s=
7 TeV and19.3 fb−1at√
s
=
8 TeV.The commonexperimental signatureofthetwo pro-cessesisapairofoppositelychargedmuonswithhightransverse momentum(pT)andasmallimbalanceofpT intheevent.TheAPprocessischaracterizedbythepresenceofadditionaljets originat-ingfrombquarks(bjets),whereastheeventswithonlyjetsfrom light quarksorgluonsare sensitive tothe GFproduction mecha-nism.Thepresenceofasignalwouldbecharacterizedbyanexcess ofeventsoverthebackgroundinthe dimuoninvariantmass cor-respondingtothe
φ
massvalue.Although the product of the cross section and the branching fractionforthe
μ
+μ
−channelisafactor103 smallerthanforthecorresponding
τ
+τ
−finalstate,themuonpaircanbefully recon-structed,andtheinvariantmasspreciselymeasuredby exploiting the excellent muon momentum resolution of the CMS detector. SearchesfortheMSSMHiggsbosonshavebeenperformedatLHC bytheLHCbexperimentintheτ
+τ
−finalstateatlarge pseudora-pidityvalues[20],theATLAS experimentintheμ
+μ
− andτ
+τ
−channels [21,22], andby the CMSexperiment in the
τ
+τ
− [23] andbb[24,25]finalstates.LimitsontheexistenceofMSSMHiggs bosonswerealsodeterminedatTevatron[26–29]andatLEP[30].Traditionally,searchesforMSSMHiggsbosonsarepresentedin the context ofbenchmark scenarios that describe the mass rela-tion among the three neutral MSSM Higgs bosons, their widths, andcrosssections.Eachscenarioassignswelldefinedvaluestothe relevantparametersoftheMSSM,exceptmA andtan
β
,whichareleft free to vary. The mmax
h benchmark scenario [19,31] provides
mh valuesaslarge as135 GeV, andtheweakestboundsontan
β
forfixedvaluesofthetopquarkmass.Forthisreason,ithasbeen usedinmostofthepreviouslyquotedanalyses topresentthe re-sultsfromMSSMHiggsbosonsearches.However,withintheMSSM thenewly discoveredstate withamassof125 GeVcanbe inter-pretedasthelightCP-evenHiggsboson,h[32].Inthiscase,alarge
partofthemA– tan
β
parameterspaceisexcludedwithinthemmaxhscenario,andnewbenchmarkswerethereforeproposed inwhich theMSSMparametersareadjustedtohavemhintheinterval122
to 128 GeV,but withawider range oftan
β
andmA values[19,31,32]. To do this, the mmax
h scenario was reformulated in two
versions,mmodh + andmmodh −, corresponding todifferent valuesof thetopsquarkmixingparameter.Otherrecentlyproposed scenar-ios[31] arethelight topsquark(lightstop)model,whichresults inamodifiedGFrate,andthelighttauslepton(lightstau)model, which yields a modified h
→
γ γ
branching fraction. Such mod-elsareexpectedmainlytoaffecttheHiggsbosonproductioncross sectionandnotthekinematicpropertiesoftheevents.A listofthe parametersofthevariousscenarioscanbefoundinRef. [23].The results presentedin thispaperare obtainedin theframework of theMSSMmmodh +scenario.Comparisonsarealsomadewithother benchmarks.2. TheCMSdetectorandeventreconstruction
The central feature of the CMS apparatus is a superconduct-ing solenoidof6 m internal diameter,providing amagneticfield of3.8 T.Withinthe solenoidvolumeare asiliconpixel andstrip tracker,aleadtungstatecrystalelectromagneticcalorimeter(ECAL), andabrassandscintillatorhadron calorimeter(HCAL),each com-prised ofa barrelandtwo endcapsections.Muonsaremeasured ingas-ionizationdetectorsembeddedinthesteelflux-returnyoke outside the solenoid. Forward calorimetry extends the coverage providedby thebarrelandendcapdetectorsuptopseudorapidity
|
η
|
<
5.AdetaileddescriptionoftheCMSdetector,togetherwitha definitionofthecoordinatesystemandkinematicvariables,canbe found inRef.[33].TheCMSofflineeventreconstruction createsa globaleventdescriptionusingtheparticleflow(PF)technique[34]. The PF eventreconstruction attemptsto reconstruct andidentify eachparticlewithanoptimizedcombinationofallsubdetector in-formation. The missing pT vector is definedasthe projection onthe planeperpendicular tothebeams ofthenegative vectorsum ofthemomentaofallreconstructedparticlesinanevent.Its mag-nitudeisreferredtoasEmiss
T .
An average of 9 and 21 pp collisions take place in any LHC bunch crossing, respectivelyat7 and8 TeV, becauseofthe large luminosity ofthemachineandthesizeofthetotalinelasticcross section. These overlapping events (pileup) are characterized by small-pT tracks, compared to the particles produced in a
φ
→
μ
+μ
−event,andtheirpresencecandegradethedetector capabil-itytoreconstructtheobjectsrelevantforthisanalysis.Theprimary vertexischosen fromall reconstructedinteractionverticesasthe one withthe largestsumin thesquaresof the pT of theassoci-atedtracks.Thechargedtracksoriginatingfromanothervertexare thenremoved.
Offline jet reconstruction is performedusing the anti-kT
clus-teringalgorithm [35,36]witha distanceparameterof0.5.The jet momentum isdefinedby thevectorialsumofallthe PFparticles momenta in thejet, andfound in simulation tobe within 5% to 10%ofthetruehadron-levelmomentum,withsome pT and
η
de-pendence.Extraenergycomingfrompileupinteractionsaffectsthe momentummeasurement.Correctionstothemeasuredjetenergy arethereforeapplied.Theyarederivedfromeventsimulation,and confirmedwithin-situmeasurementsusingenergybalanceindijet andZ/photon
+
jetevents[37].Muonsaremeasuredinthepseudorapidityrange
|
η
|
<
2.
4, us-ingdetectionplanesbasedonthreetechnologies:drifttubes, cath-odestripchambers,andresistive-platechambers.Matchingmuons totracksmeasuredinthesilicontrackerprovidesrelativepTTable 1
ThemAandtanβvaluesusedtogeneratesignalsamples.
mA(GeV) mAstep (GeV) tanβ tanβstep
115–200 5 5–55 5
200–300 25 5–55 5
300–500 50 5–55 5
andbetterthan6%intheendcaps.The pT resolutioninthebarrel
isbetterthan10%formuonswithpT upto1 TeV[38].
3. Simulatedsamples
Simulatedsamplesareused tomodel thesignal andto deter-minetheefficiencyofthesignalselection.Backgroundsamplesare alsosimulatedtooptimizetheselectioncriteria.Thenormalization anddistributionofthebackgroundeventsaremeasuredfromdata. Thesignal samples aregenerated usingthe MonteCarlo(MC) eventgenerator pythia 6.424[39]forawiderangeofmAandtan
β
values,aslistedinTable 1,fortheAPandtheGFproduction mech-anisms.The
φ
production cross sectionsandtheir corresponding uncertaintiesareprovidedbytheLHCHiggsCrossSectionWorking Group[16–18].ThecrosssectionsfortheGFprocessinthemmaxh scenario are obtained using the HIGLU program [40,41], based on next-to-leadingorder (NLO) quantum chromodynamics (QCD) calculations.The sushi program[42] isusedfortheother bench-marks.FortheAPprocess,thefour-flavorNLOQCDcalculation[43, 44]andthefive-flavor next-to-next-to-leadingorder(NNLO) QCD calculationareimplementedin bbh@nnlo[45]andcombined us-ingthe Santandermatchingscheme[46].TheHiggsYukawa cou-plings computed with the feynhiggs program [47] are used in the calculations. The decay branching fractions to muons in the different benchmark scenarios are obtained with feynhiggs and hdecay[48].Furtherdetailson signalgeneration canbe foundin Refs.[16–18].Thevalues ofmh predicted by feynhiggs differtypically by a
few GeV from those computed with pythia. The invariant mass spectrumof the h boson istherefore shifted tomatch the feyn-higgsprediction.The smalldifference between pythia and feyn-higgs in assessing the width of the h boson is of the order of 100 MeV, and therefore neglected, since the experimental mass resolution is at least one order of magnitude larger. The pythia parametersusedtosimulatethesignalarethoseforthemmax
h
sce-nario.SinceforagivensetofmA andtan
β
values,thekinematicpropertiesofthefinalstate arethesameforallthescenarios,the simulatedsamplesbasedonthemmax
h benchmarkarealsousedto
checkthevalidityoftheothermodels.Furtherdetailsonthis pro-cedure and the related systematic uncertainties are discussed in Section7.
Themain source ofbackground forthe
φ
production and de-cay toμ
+μ
− isDrell–Yan muon-pairproduction, qq¯
→
Z/
γ
∗→
μ
+μ
−.Anotherbackgroundisfromoppositelychargedmuonpairs produced indecays of top quarks in t¯
t production. Theseevents aresimulatedusingthe MadGraph 5.1[49]generator.Other back-groundprocessessuchasW±W∓,W±Z,andZZ aregeneratedwith pythia. The MC samples also includesimulated pileup events to reproducetheoverlappingppinteractions presentinthedata.All generated events are processed through a detailedsimulation of theCMSdetectorbasedon Geant4[50]andarereconstructedwith thesamealgorithmsusedfordata.4. Eventselection
The experimental signature of the MSSM Higgs bosons decay consideredin thisanalysisisa pairofoppositely chargedmuons
Table 2
Eventselection:thecriterialistedintheupperpartofthetablearecommontothe C1andC2categories,thatarethenmutuallyexclusive.
Common selection
Single muon trigger pT>24 GeV+isolation+ |η| <2.1
Event primary vertex |zPV| <24 cm
Muon selection 2 opposite-charged muons,
pT>24 GeV,|η| <2.1,
track quality cuts,
|dxy| <0.02 cm,|dz| <0.1 cm,
angular matching with trigger, isolation Emiss T E miss T <35 GeV Category C1
b tag 1 or 2 b-tagged jets,
pjetT >20 GeV,|ηjet| <2.4
Category C2
No b tag Events with no b-tagged jets
with high pT. The invariant mass of the paircorresponds to the
massofthe
φ
bosonwithintheexperimentalresolution.Moreover, theprocessischaracterizedbyasmallEmissT intheevent.Iftheφ
bosonisproducedinassociationwithabb pair,thepresenceofat leastonebquarkjetisexpected.
Thedetailsoftheeventselectionarelistedbelow,and summa-rizedinTable 2.Theeventsareselectedusingasingle-muon trig-ger,whichrequiresatleastone isolated muonwith pT
>
24 GeVinthepseudorapidityrange
|
η
|
<
2.
1.Thedistanceoftheprimary vertex along the z axisfrom the nominalcentre of the detector must be|
zPV|
<
24 cm. Muon candidates are reconstructed andidentifiedusingboththeinner trackerandthemuondetector in-formation.Theselectedeventsmusthaveatleasttwo oppositely-chargedmuoncandidates,each withpT
>
25 GeV.Ineventswithmore than two muon candidates, the two withopposite charges andthe highest pT are retained.The
η
of both muoncandidatesischosen tomatchthetriggeracceptance.Eachmuontrackmust haveatleastonehitinthepixeldetector,morethanfiveoreight layers with hits inthe tracker, respectively, for the 8 and7 TeV data and a directional matching to hits in at leasttwo different muondetectorplanes.Inadditiontheglobalfittothehitsofthe muon candidate must include at least one hit in the muon de-tector. The
χ
2/
dof of the global fit of the muon track must besmallerthan 10.Theserequirementsensure agoodmeasurement ofthemomentum,andsignificantlyreducetheamountofhadronic punch-through background [38]. Toreject cosmic ray muons, the transverseandlongitudinalimpactparametersofeachmuontrack mustsatisfy the requirements
|
dxy|
<
0.
02 cm and|
dz|
<
0.
1 cm,respectively. Both parameters are definedrelative to the primary vertex.Toensurethatthetriggermuoncandidateiswell-matched to the reconstructed muon track, at least one of the two muon tracks isrequiredto matchthe directionofthetrigger candidate within a cone
R
=
0.
2, whereR
=
√
[
b](
η
)
2+ (
ϕ
)
2 is the distancebetweenthemuontrackandthetriggercandidate direc-tionintheη
–ϕ
plane,withϕ
beingtheazimuthalanglemeasured inradians. Bothreconstructed muoncandidatesmust fulfill isola-tion criteria. A muon isolation variable is constructed using the scalar sum of the pT of all PF particles, except the muon,re-constructed within a cone
R
=
0.
4 around the muon direction. Acorrection isapplied to accountforthe possiblecontamination fromneutralparticlesarising frompileup interactions.Amuon is acceptedifthevalueofthecorrectedisolationvariableislessthan 12%ofthemuonpT.A selection based on EmissT provides good separation between signal eventsand t
¯
t background,in thecaseof leptonic decayofFig. 2. TheEmiss
T distributionforeventswithareconstructeddimuoninvariantmass
mμ+μ−>60 GeV indataandinsimulatedeventsat√s=7 (top)and√s=8 TeV (bottom).TheexpectedcontributionisalsoshownforasignalatmA=150 GeV and
tanβ=30.
the W boson from top decay. The EmissT distributions for events collectedat
√
s=
7 and8 TeVareshowninFig. 2foreventswith areconstructedmuon pairwithinvariant massmμ+μ−>
60 GeV. The background contributions from SM processes are superim-posed. For illustration, the expected distribution for signal pro-cesses is also shown formA=
150 GeV and tanβ
=
30. Studiesperformedusing the simulation show that the EmissT distribution forsignal eventsdoesnot vary significantly fordifferentmA and
tan
β
assumptions,andindicatethat theselection EmissT<
35 GeV provideshighestsensitivityforsignalatbothcentre-of-mass ener-gies.Thereconstructedjetsarerequiredtohavetransversemomenta pjetT
>
20 GeV within the range|
η
|
<
2.
4. A multivariate analysis techniqueisusedtoremovejetsfrompileupinteractions[51]. Tag-gingof bquarks injetsrelieson thecombined secondary-vertex discriminator [52],based on the reconstruction of the secondary vertex from weakly decaying b hadrons. The discriminant bdiscisconstructedfromtracks andsecondary vertexinformation,and helpsto distinguishjets containing b,c,or light-flavourhadrons. Jetswithanassociatedbdisc
>
0.
679 areconsideredtobebtagged.Thisvaluerepresentsagoodcompromisebetweenefficiencytotag bjetsinsignaleventsfromAP(
≈
80%)andmistaggingprobability forlight-quarkjets(≈
1%).Fig. 3showsthedistributionofbdisc inFig. 3. Thedistributionofthebtaggingdiscriminant,bdisc,foreventsthatsatisfythe
selectionEmiss
T <35 GeV indatacollectedat
√
s=7 (top)and√s=8 TeV (bottom). Foreachevent,thelargestvalueofbdiscisselected.
eventsthat satisfy theselection Emiss
T
<
35 GeV,forthedatacol-lected inthetwobeamenergies.Foreachevent,thelargestvalue of bdisc is selected.The distribution ofsignal eventsfrom theAP
process for mA
=
150 GeV and tanβ
=
30 is superimposed. Jetsoriginated from b quark fragmentation tend to be emitted more forwardinsignaleventsthan fort
¯
t,thus resultinginalower ob-served b-jetmultiplicity.Forthisreasonthet¯
t backgroundis fur-thersuppressedbyrejecting eventswithmorethantwob-tagged jets, withoutsignificantly affectingtheselectionefficiencyfor sig-nal.Theeventsaresplitintotwomutually-exclusivecategories.The first category(C1)contains eventswithatleastonejet identified asoriginatedfromb-quarkfragmentation(btagged),andprovides highest sensitivity to AP production channel. Events that do not containb-taggedjetsare assignedtocategory2(C2),andprovide sensitivityto GFproduction.The dimuoninvariant mass distribu-tions for the C1 and C2 categories are shown in Fig. 4 for data and simulated events for both centre-of-mass energies. The dis-tributions expected forMSSM Higgs bosons with mA
=
150 GeVand tan
β
=
30, derived from the mmodh + scenario are also given forcomparison.Adoublepeakstructurearound125and150 GeV appears intheC2category,duetothehboson andA+
H bosons, respectively.The lowerpeakisnot visibleinC1,astheh produc-tionissuppressedintheAPmechanismrelativetotheGFprocess.Fig. 4. ThedimuoninvariantmassdistributionforeventsthatbelongtoC1(upperleft)andC2category(upperright),fordataandsimulatedeventsat√s=7 TeV.The correspondingquantitiesareshownfor√s=8 TeV (lowerleftandlowerright).Theexpectedcontributionstosignalassumingthemmodh +scenarioformA=150 GeV and
tanβ=30 aredisplayedforcomparison.
5. Signalselectionefficiency
WhilethecalculationsfortheMSSMcross sectionsperformed inthenarrow-widthapproximationrefertotheon-shellHiggs bo-son production,at large values of mA and tan
β
the convolutionofthe larger intrinsicsignal widths withthe parton distribution functions(PDF)resultsinanon-negligiblefractionofsignalevents producedsignificantlyoff-shell.Eventswithinvariantmass signifi-cantlysmallerthanitsnominalvaluehavealower reconstruction efficiency than those produced near the mass peak. For consis-tency, we define signal efficiency as the probability for a signal eventwiththegeneratedinvariantmassclosetoitsnominalvalue to be reconstructed and pass all selection requirements of this analysis.Theclosenessisdefinedusingawindowofsizeequalto 3timesthe intrinsicsignal width(anuncertaintyassociatedwith thisdefinitionis evaluated usinga windowof 5times its width, asdiscussedinSection7).Withthisdefinition,theproductofthe MSSMHiggsbosonproductioncrosssection,luminosityandsignal efficiencyprovidesthenormalizationfortheHiggsbosonproduced near on-shell. The full predicted rate of signal events also con-tains an additional off-shell contribution, which varies with mA
andtan
β
andislessthan 5% formA<
250 GeV and tanβ <
15,andcanbeaslargeas15%formA
=
300 GeV andtanβ
=
30.Additional corrections are applied to the signal efficiency to takeintoaccount differencesbetweendataandsimulationinthe muon trigger, reconstruction, and isolation efficiencies. A
correc-tionisalsoappliedtoaccountforknowndata-simulation discrep-ancies inthe btaggingefficiencyandmistaggingprobability.The correctionsaresummarizedby aweight factor,whichisassigned toeach signal event.The averageoftheweight factorscomputed overalltheeventsisveryclosetoone,reflectingthefactthatthe simulationdescribesthedatawithgoodaccuracy.
Fig. 5 showsthe signal efficiencyat
√
s=
8 TeV for AP (top) andGF(bottom)processaftercombiningthetwoeventcategories C1andC2.Theefficienciesat√
s=
7 TeV aresimilar.Thebandin thefigurerepresentsthevariationoftheefficiencyduetothe lim-itedstatistics ofthesamplesused.TherelativeamountofAPand GFevents inthe two eventcategoriesvarieswithmA and tanβ
,since the production crosssections ofthe two processes depend ontheseparameters.Forexample,inthecasemA
=
150 GeV andtan
β
=
30, more than 90% of the signal events in C1 would be fromAPproduction,andabout60%inC2.FormA=
150 GeV andtan
β
=
5,wherethe GFcontribution becomesmore relevant,the contentofAPeventswouldbe60%inC1andonly15%inC2. 6. FitprocedureTheproceduredescribedbelowisappliedseparatelytoC1and C2 events. The event selection criteria are applied to the simu-latedsamples listedin Table 1. Foreach sample, andforeach of the three
φ
bosons, theinvariant massdistribution ofthe events thatpasstheeventselectionisapproximatedwithaBreit–WignerFig. 5. SignalefficiencyfortheAPprocessat√s=8 TeV,shownseparatelyforthethreeφbosontypes,(upperleft)h,(uppercentre)H,and(upperright)A,asafunction ofmA.ThecorrespondingefficiencyfortheGFproductionprocessisshowninthelowerrow.ThecontributionsfromthetwoeventcategoriesC1andC2arecombined.
Theresultsareintegratedovertanβ,sincetheefficiencydoesnotstronglydependonthisquantity.Thebandshowsthechangeinefficiencyduetothelimitednumberof simulatedevents.
functionconvolvedwithaGaussian,thataccountsfordetector res-olution. This analyticalexpression provides a good description of thesignal shapeforall themA andtan
β
values.The threefunc-tionsaredenotedFh,FH,andFA,andcontainthemassandwidth
oftheBreit–WignerandthewidthoftheGaussianasfree param-eters.ThefunctionFsigrepresentstheexpectedsignalyield,andit
isalinearcombinationofthethreefunctionsdescribedabove:
Fsig
=
whFh+
wHFH+
wAFA,
(2)wherewh,wH,andwA,arethenumberofeventscontainingh,H,
andAbosons,respectively, calculatedaccordingtotheir expected productioncrosssections.Anexampleofthisprocedureisshown inFig. 6(top)formA
=
150 GeV and tanβ
=
30.Thehighestpeakrepresents the superposition of the contributions from H and A bosons,thatinthiscasearealmostdegenerateinmass.
Since the Drell–Yan muon pair production is the dominant backgroundprocess,itismodeledbyaBreit–Wignerfunctionplus aphoton-exchangeterm,whichisproportionalto1
/
m2μ+μ−.Defin-ingm
=
mμ+μ−,thefunctionFbkg becomes:Fbkg
=
eλm⎡
⎣
fZ N1norm 1(
m−
mZ)
2+
2 Z 4+
(
1−
fZ)
Nnorm2 1 m2⎤
⎦ ,
(3)whereeλm describestheeffects ofthePDF, andthe Nnormi terms correspond to the integral ofthe corresponding functionsin the chosenmassrange.Thequantity fZrepresentsthecontributionof
theBreit–Wigner termrelativetothe photon-exchangeterm. The quantities
λ
and fZ arefreeparametersofthefit.TheparametersZ andmZaredeterminedseparatelyfortheC1andtheC2events
from a fitto themμ+μ− distributionin the massrange ofthe Z bosonbetween80and120 GeV.Thefitprovidestheeffective val-uesofsuchquantities,thatincludedetectorandresolutioneffects for each set of data. Their valuesare used in Fbkg andare kept
constantinthefit.
Alinearcombinationofthetwofunctionsfortheexpected sig-nal andbackgroundisthenused inan unbinnedlikelihoodfit to thedata:
Ffit
= (
1−
fbkg)
Fsig+
fbkgFbkg.
(4)The parametersthat describethesignal aredetermined inthe fitofthesimulatedsignaltoEq.(2),foreachpairofmA andtan
β
values.Subsequently,theyarefixedinFfit,wherethefree
parame-tersarethequantities
λ
, fZ,and fbkg.Thefractionofsignaleventsis defined as fsig
= (
1−
fbkg)
. The data are fittedto Ffit in themass range from 115to 300 GeV for each point in the mA and
tan
β
parameterspace. Asanexample,thefittothedataofC2at√
s
=
8 TeV isillustratedinFig. 6,(bottom),assumingasignalwith mA=
150 GeV andtanβ
=
30.7. Systematicuncertainties
Thefollowingsourcesofsystematicuncertaintiesaretakeninto account, and the impact ofone standard deviationchange is re-ported in terms of a variation in the nominal signal efficiency definedinSection5.
The limited number of simulated events introduces an un-certainty in the signal selection efficiency that is at most 2.0%. The muon trigger, reconstruction, identification, andisolation ef-ficiencies are determined fromdata using a tag-and-probe tech-nique [38].The uncertainty in the triggerefficiency correction is
Fig. 6. InvariantmassdistributionoftheexpectedsignalformA=150 GeV and
tanβ=30 (top),andanexampleofthefittothedataat√s=8 TeV includingthe samesignalassumption(bottom).Thedistributionrepresentstheexpectednumber ofeventsforanintegratedluminosityof19.3 fb−1.Foreachplotthepullofthefit
asafunctionofthedimuoninvariantmassisshown.
0.5%,whereas1.0%isassignedtothecombinationofuncertainties inmuonreconstruction andidentification, aswell asonisolation efficiencies.
Asystematicuncertaintyinthepileupmultiplicityisevaluated by changing the total cross section for inelastic pp collisions in simulation.Thecorresponding uncertaintyonthesignalefficiency isatmost0.8%inbothcategories.
Theeventfractionsinthetwocategoriesdependontheb tag-gingefficiencyandthemistaggingprobability.The uncertaintyin thebtaggingefficiencyisestimatedby comparingdataand sim-ulatedeventswithsamples ofenriched b quark contentand dif-ferenttopologies,asdescribedinRef.[52].The uncertaintyinthe efficiencyto detectbjetsisabout3.0%.Similarly,theuncertainty inthemistagging rateisabout10%. Theiroverall contributionto theselection efficiencyis weighted by thefraction ofAPandGF eventsthat are expected in each eventcategory, which depends onmAandtan
β
.Thelargestoveralluncertaintyis3.0%forC1,and0.4%forC2events.
Thejet energyscale uncertaintyis estimatedbysmearing the jetmomentumbya factordependingon pT and
η
ofeachjet, asdescribed in Ref. [37]. The effecton signal selection efficiencyis 4.0% forevents that belong to the C1 and 0.5% for the C2 cate-gories,at
√
s=
8 TeV.For√
s=
7 TeV thecorrespondingnumbers are3.8% and0.6%.The uncertaintyinthe EmissT scaleand
resolu-tionisestimatedthrough comparisonsbetweendataand
simula-Table 3
SourcesofsystematicuncertaintiesforC1andC2eventcategoriesthataffectthe signal efficiencyat √s=8 TeV.They areexpressed interms ofrelative signal selectionefficiency.Whenthesystematicuncertaintyat√s=7 TeV differsfrom
√
s=8 TeV,thecorrespondingvalueisquotedinparenthesis. Source Systematic uncertainty (%)
C1 C2 MC statistics 2.0 2.0 Trigger efficiency 0.5 0.5 Muon efficiency 1.0 1.0 Muon isolation 1.0 1.0 Pileup 0.8 0.8 b tagging 3.0 0.4
Jet energy scale 4.0 (3.8) 0.5 (0.6)
Emiss
T 3.0 (2.0) 3.0 (2.0)
Integrated luminosity 2.6 (2.2) 2.6 (2.2)
PDFs 3.0 3.0
Width correction 1–3 1–5
tion[53,54].Theeffectonthesignalselectionefficiencyis3.0%and 2.0%,thesameforbothcategories,forthesamplewith
√
s=
8 and 7 TeV,respectively.Theuncertaintyintheintegratedluminosityis 2.6%and2.2%at√
s=
8 and7 TeV,respectively[55,56].UncertaintiesduetothechoiceofPDFsetaffectthesignal effi-ciency, andare studiedusing thePDF4LHC [57] prescription.The renormalization and factorization scales in the calculations and their changes aresummarized inRefs. [16–18].The effecton the signalselectionefficiencyvariesfrom1.0%to3.0%overthemAand
tan
β
parameterspace. Thechoiceof3.0%istakenasthe system-aticuncertainty.The efficiency is determined for events with generated mass valueswithin awindow ofa factorof3ofthe intrinsicwidthof theHiggsboson,asdescribedinSection5.Thedifferencerelative to the efficiency obtained using a cutoff of a factor of 5 of the intrinsicwidthisassignedasasystematicuncertainty.The uncer-tainty is between1% to 3% forthe C1 and1% to 5% for the C2 categories.
Table 3lists thesystematicuncertainties thataffectthe deter-minationofsignalefficiency.Theimpactofthesesystematic uncer-taintiesontheexclusionlimitsthatwillbepresentedinSection8 is negligible compared to the statistical uncertainty. All the sys-tematicuncertaintiesinTable 3arecorrelatedforthe
√
s=
7 TeV and8 TeVdata,withtheexceptionoftheuncertaintiesrelatedto thelimitedMCstatisticsandtheintegratedluminosity.The uncertainties inthe MSSM cross sections depend onmA,
tan
β
,andthescenario,andare providedby theLHCHiggsCross Section Working Group [16–18]. The signal eventsare generated using pythia, assuming the parameters of the mmaxh scenario, as discussed inSection 3.The differentbenchmarksareexpectedto affecttheproductioncrosssection,butnotthekinematic proper-tiesoftheeventsrelatedtoHiggsbosonproductionanddecay.To checkthisassumption,eventsaregeneratedwith pythia usingthe parametersforthemmodh +,mhmod−,lightstopandlightstau bench-marks, assuming mA=
150 GeV and tanβ
=
20. The events aregeneratedforboththeGFandtheAPmechanisms,andtheHiggs boson pT andthe EmissT of theevents are comparedat generator
level for the various benchmark scenarios. No significant differ-encesareobservedinthedistributionsofthesequantities.
Sincethenumberofbackgroundeventsisdeterminedthrough a fittothedata,an additionalsystematicuncertaintyarisesfrom the possibility that the background parametrizationmay not ad-equately describe thedata asa functionof thedimuon invariant mass. Amethod similar to that described inRef. [10] is used to evaluatetheeffect,byestimatingtheuncertaintythroughthebias intermsofthenumberofsignal eventsthat arefound when
fit-tingthesignal
+
backgroundmodel(asdescribed inSection6)to pseudo-datagenerated for different alternative background mod-els. Such alternative background parametrizations include Bern-stein polynomials and combinations of Voigtian and exponential functions. Bias estimatesare performed formasspoints between mA=
115 and300 GeV.ForeachmAvalue,thelargestbiasamongthetestedfunctionsistakenastheresultinguncertainty.Thebias isimplementedasa floatingadditive contributiontothenumber ofsignalevents,constrainedbyaGaussianprobabilitydensitywith mean of zero and width set to the systematic uncertainty. The width of the Gaussian is the largest systematicuncertainty, and the effectis to increase the expected limit on the presence ofa signalby20%intheregionnearmA
=
120 GeV andbyabout10%atlargermassvalues.
Inthe massrangebetween115and300 GeV,that isrelevant forthisanalysis, the mass resolutionis estimatedto be between 1.2and4 GeV.Uncertaintiesinthemuonmomentum determina-tion can affect the invariant mass measurement, and have been carefullystudiedin dataandsimulation[38].The dimuon invari-antmassresolutionformassesabovethe Zpeakhasbeen previ-ouslystudied inthesearch fora SMHiggs decayingtoadimuon pair[58].ThemassresolutiondeterminedfromdataattheZmass value is 1 GeV, in excellent agreement withthe prediction from simulation. This value is consistent with the mass resolution of 1.2 GeVthatwe estimatefromsimulationforamassof115 GeV, thatcorresponds tothelower edgeofthe Higgsmassrange con-sideredinthisanalysis.
Theoverallcapabilityoftheanalysistodetectthepresenceofa signalisverifiedbyintroducingahypotheticalsimulatedsignalin the datausing the shape parametrizationdiscussed inSection 6. The average measured number of signal events is found to be within1.3% oftheinjectedsignal fortheC1category, andwithin 4.3%fortheC2category.Thesedifferencesareassignedas system-aticuncertainties.
8. Results
No evidenceofMSSM Higgsbosons productionisobservedin the mass range between 115 and 300 GeV, where the analysis has been performed. Upper limits at 95% confidence level (CL) on theparameter tan
β
are computedusingthe CLs method[59,60], which is a modified frequentist criterion, andare presented as a function of mA. Systematic uncertainties are incorporated
as nuisance parameters andtreated according to the frequentist paradigm [61]. The results are obtained from a combination of botheventcategoriesandcentre-of-massenergies.Foreachvalue ofmA,the value oftan
β
atwhichthe CLexceeds 95%is chosentodefinetheexclusionlimitonthatmA.Thisisperformedforall
themA values andthe resultsare shownin Fig. 7.These results
areobtainedwithin themmodh +scenario.Theobservedupper lim-itsrangefromtan
β
ofabout15inthelow-mAregion,toabove40atmA
=
300 GeV.Forlarger valuesofmA theuncertaintyonthetan
β
upperlimit becomes large,exceeding tanβ
=
50,for which theMSSMcross-sectionpredictionsarenotreliable.Acomparison withtheresults obtainedforthe mmodh −,mmaxh , lightstopandlightstauscenariosisalsoperformed.Theexclusion limitscomputedwithintheseotherbenchmarkmodelsareallvery similar. Foranyvalue ofmA,the quantity
tan
β
=
tanβ
mmod+h
−
tan
β
scenario representsthedifferenceofthetanβ
valuesatwhichthe95% CL limit isdetermined ifan alternative scenariois used. Fig. 8 showsthequantity
tan
β
asa function ofmA forallthetestedscenarios. FormostmA values,the 95% CLlimitson tan
β
computedwithinagivenscenariodifferbylessthanoneunitfrom theresultsobtainedwithinthemmodh + scenario.
Fig. 7. The95%CLupperlimitontanβasafunctionofmA,aftercombiningthedata
fromthetwoeventcategoriesatthetwocentre-of-massenergies(7and8 TeV).The resultsareobtainedintheframeworkofthemmodh +benchmarkscenario.
Fig. 8. Comparisonofthe95%CLexclusionlimitsontanβobtainedwithinMSSM benchmark models, as a function ofmA. The quantity tanβ=tanβmmod+
h −
tanβscenariorepresentsthedifferenceintanβatwhichthe95%CLlimitisobtained
foralternativescenarios.
Limits on the productioncross section times decay branching fraction
σ
B(φ →
μ
+μ
−)
for a generic single neutral bosonφ
aredetermined.Inthismodelindependentanalysisnoassumption is made on the cross section, mass, andwidth of the
φ
bosons, which is sought as a single resonance with mass mφ. The anal-ysis isperformed assuming thenarrow widthapproximation, for whichtheintrinsicwidthofthesignalissmallerthanthe invari-ant massresolution.For thispurposethesimulated signal ofthe A boson for the case tanβ
=
10 is used as a template to com-pute thedetectionefficiencyfora genericφ
boson decayingto a muonpair.Thesingleφ
bosonisassumedtobeproducedentirely either via the AP or the GFprocess, and the search for a single resonance with massmφ is performed. The 95% CL exclusion onσ
B(φ →
μ
+μ
−)
is determined as a function of mφ, separately for the two production mechanisms. The combination of events belonging to C1 andC2 is shown in Fig. 9, assuming theφ
bo-son is produced either via the AP or the GF process. Only data collected at√
s=
8 TeV are used,asthey providea better sensi-tivity because of the higher luminosity. In addition, since theφ
production cross section depends on the centre-of-mass energy, a combination with the 7 TeV results would introduce a model
Fig. 9. The95%CLlimitontheproductofthecrosssectionandthedecaybranching fractiontotwomuonsasafunctionofmφ, obtainedfromamodelindependent
analysisofthedata.Theresultsreferto(top)bquarkassociatedand(bottom)gluon fusionproduction,obtainedusingdatacollectedat√s=8 TeV.
dependenceinthedescriptionofthecrosssectionevolutionwith energy.
9. Summary
Asearch has beenperformed forneutralMSSM Higgs bosons decayingto
μ
+μ
− frompp collisionscollected withtheCMS ex-perimentat√
s=
7 and8 TeV,corresponding tointegrated lumi-nositiesof5.1and19.3 fb−1,respectively.Theanalysisissensitive to Higgs boson production via gluon fusion, and via association witha bb quark pair. The results ofthe search, whichhas been performedinthemassrangebetween115and300 GeV,are pre-sentedinthe mmodh + framework of theMSSM.With noevidence forMSSM Higgs boson production, this analysisexcludes at 95% CL values of tanβ
larger than 40 for Higgs boson masses up to 300 GeV.Comparisonswithmmodh −,mmaxh ,lightstop,andlightstau scenariosarealsopresented,andofferverysimilarresultsrelative to themmodh + benchmark. Limits are determined on the product ofthecrosssectionandbranchingfractionσ
B(φ →
μ
+μ
−)
fora genericneutralbosonφ
at√
s=
8 TeV, withoutanyassumptions ontheMSSMparameters.Inthiscasetheφ
bosonisassumedto beproducedeitherinassociationwithabb quarkpairordirectly throughgluonfusion,andsoughtasasingleresonancewithmass mφ.Exclusionlimitsareinthemassregionfrom115to500 GeV. Formφ=
500 GeV,valuesσ
B(φ →
μ
+μ
−)
>
4 fb areexcludedat 95%CLforbothproductionmechanisms.Thesearethemost strin-gentresultsinthedimuonchanneltodate.Acknowledgements
WecongratulateourcolleaguesintheCERNaccelerator depart-ments for the excellent performance of the LHC and thank the technicalandadministrative staffsatCERN andatother CMS in-stitutes for their contributions to the success of the CMS effort. Inaddition,wegratefullyacknowledgethecomputingcentresand personneloftheWorldwideLHCComputingGridfordeliveringso effectivelythe computinginfrastructureessential to ouranalyses. Finally, we acknowledge the enduring support for the construc-tion and operation of the LHC and the CMS detector provided by the following funding agencies: BMWFW and FWF (Austria); F.R.S.- FNRS andFWO(Belgium);CNPq,CAPES,FAPERJ,andFAPESP (Brazil);MES(Bulgaria);CERN;CAS,MOST,andNSFC(China); COL-CIENCIAS(Colombia);MSESandCSF(Croatia);RPF(Cyprus);MoER, ERC IUT and ERDF (Estonia); Academy ofFinland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NIH (Hungary); DAE and DST (India);IPM(Iran); SFI(Ireland);INFN (Italy); NRF andWCU (Republic of Korea); LAS (Lithuania); MOE and UM (Malaysia); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portu-gal);JINR(Dubna);MON,RosAtom,RASandRFBR(Russia);MESTD (Serbia);SEIDIandCPAN(Spain);SwissFundingAgencies (Switzer-land); MST (Taipei); ThEPCenter, IPST, STAR and NSTDA (Thai-land);TUBITAKandTAEK(Turkey);NASUandSFFR(Ukraine);STFC (UnitedKingdom);DOEandNSF(USA).
Individuals have received support from the Marie-Curie pro-gramme and the European Research Council and EPLANET (Eu-ropean Union); the Leventis Foundation; the A. P. Sloan Founda-tion; the Alexander von Humboldt Foundation; the Belgian Fed-eral Science Policy Office; the Fonds pour la Formation à la Recherchedansl’Industrieetdansl’Agriculture(FRIA-Belgium);the AgentschapvoorInnovatiedoorWetenschapenTechnologie (IWT-Belgium); theMinistry ofEducation, YouthandSports (MEYS) of theCzechRepublic;theCouncilofScienceandIndustrialResearch, India; the HOMING PLUS programme of Foundation for Polish Science, cofinanced from European Union, Regional Development Fund;the CompagniadiSan Paolo(Torino); the Consorzioper la Fisica (Trieste); MIURproject20108T4XTM (Italy);the Thalisand Aristeia programmes cofinanced by EU-ESF andthe Greek NSRF; the National Priorities Research Program by Qatar National Re-search Fund;theRachadapisekSompot FundforPostdoctoral Fel-lowship,ChulalongkornUniversity(Thailand);andtheWelch Foun-dation.
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T. Caebergs,
G.H. Hammad
UniversitédeMons,Mons,Belgium
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G.A. Alves,
L. Brito,
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Y. Ban,
Q. Li,
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N. Godinovic,
D. Lelas,
D. Polic,
I. Puljak
UniversityofSplit,FacultyofElectricalEngineering,MechanicalEngineeringandNavalArchitecture,Split,Croatia
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UniversityofSplit,FacultyofScience,Split,Croatia
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InstituteRudjerBoskovic,Zagreb,Croatia
A. Attikis,
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H. Rykaczewski
UniversityofCyprus,Nicosia,Cyprus
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B. Calpas,
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NationalInstituteofChemicalPhysicsandBiophysics,Tallinn,Estonia
P. Eerola,
M. Voutilainen
DepartmentofPhysics,UniversityofHelsinki,Helsinki,Finland
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V. Karimäki,
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E. Tuominen,
J. Tuominiemi,
E. Tuovinen,
L. Wendland
J. Talvitie,
T. Tuuva
LappeenrantaUniversityofTechnology,Lappeenranta,Finland
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N. Chanon,
C. Collard,
E. Conte
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InstitutPluridisciplinaireHubertCurien,UniversitédeStrasbourg,UniversitédeHauteAlsaceMulhouse,CNRS/IN2P3,Strasbourg,France
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17GeorgianTechnicalUniversity,Tbilisi,Georgia
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H. Weber,
B. Wittmer,
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M. Brodski,
E. Dietz-Laursonn,
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S. Erdweg,
T. Esch,
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C. Heidemann,
K. Hoepfner,
D. Klingebiel,
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P. Millet,
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M. Radziej,
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D. Teyssier,
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Y. Erdogan,
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O. Pooth,
A. Stahl
RWTHAachenUniversity,III.PhysikalischesInstitutB,Aachen,Germany